Fekete–Szegő and Zalcman Functional Estimates for Subclasses of Alpha-Convex Functions Related to Trigonometric Functions

Krishnan Marimuthu, Uma Jayaraman and Teodor Bulboacă ()
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Krishnan Marimuthu: Department of Mathematics, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Chennai 600062, Tamilnadu, India
Uma Jayaraman: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamilnadu, India
Teodor Bulboacă: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 2, 1-13

Abstract: In this study, we introduce the new subclasses, M α ( sin ) and M α ( cos ) , of α -convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions that belong to these classes. Further, we determine the upper bound of the Zalcman functional for the class M α ( cos ) for the case n = 3 , proving that the Zalcman conjecture holds for this value of n . Moreover, the problem of the Fekete–Szegő functional estimate for these classes is studied.

Keywords: analytic functions; subordination; Carathéodory functions; sine function; cosine function; alpha-convex functions; starlike and convex functions; coefficient bounds; Fekete–Szeg? functional; Zalcman functional (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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